In the Yoga Vasishta, Sage Vasishta answers the queries of Lord Ram. The questions raised by Lord Ram pertain to problems like life and death, human suffering, desire, happiness etc. The original Yoga Vaishta consists of 32,000 shlokas. This particular version that is available for download is the translation of Laghu Yoga Vasishta - it contains 6000 verses and is an abridgement of the original. This pdf format of Yoga Vasishta is of a book on Laghu Yoga Vasishta written by K Narayana Swami Aiyer and was first published in 1896.
You can find the book here at archive.org - Yoga Vasishta Translation in English
Alternatively you can go for the pdf format directly here - Yoga Vasishta English in PDF format
Please note that the PDF format is nearly 40 MB and you will need Adobe Acrobat.